Spinfoam models (see \(\textit {e.g.}\)  [1]}, [2]}, [3]} for reviews) provide a rigorous, background-independent and non-perturbative path integral quantization of gravitational theories based on discrete topological quantum field theories and state-sum models. They define probability amplitudes for histories of quantum states of geometry defined as entangled collections of discrete excitations.
They can be considered as a quantum version of Regge calculus for discretized general relativity [4]}. They provide transition amplitudes for spin network states in loop quantum gravity [5]}, [1]}, [7]}. They also provide the triangulation weights in sum-over-random-geometries approaches to quantum gravity, such as matrix models, tensor models and group field theories [8]}, [9]}. Finally, they are a natural mathematical framework for defining topological invariants \(\textit {e.g.}\)  [10]}, and have been shown to be related to non-commutative geometry, \(\textit {e.g.}\)  [11]}, to lattice field theories with quantum group gauge symmetries, \(\textit {e.g.}\)  [12]}, [13]}, and to higher gauge theories [14]}, [15]}, [16]}, [17]}.
